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Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies

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  • Antonello Maruotti
  • Antonio Punzo

Abstract

The expectation–maximization (EM) algorithm is a familiar tool for computing the maximum likelihood estimate of the parameters in hidden Markov and semi‐Markov models. This paper carries out a detailed study on the influence that the initial values of the parameters impose on the results produced by the algorithm. We compare random starts and partitional and model‐based strategies for choosing the initial values for the EM algorithm in the case of multivariate Gaussian emission distributions (EDs) and assess the performance of each strategy with different assessment criteria. Several data generation settings are considered with varying number of latent states, of variables as well as of the level of fuzziness in the data, and discussion on how each factor influences the obtained results is provided. Simulation results show that different initialization strategies may lead to different log‐likelihood values and, accordingly, to different estimated partitions. A clear indication of which strategies should be preferred is given. We further include two real‐data examples, widely analysed in the hidden semi‐Markov model literature.

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  • Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:3:p:447-480
    DOI: 10.1111/insr.12436
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    1. Antonello Maruotti, 2011. "Mixed Hidden Markov Models for Longitudinal Data: An Overview," International Statistical Review, International Statistical Institute, vol. 79(3), pages 427-454, December.
    2. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    3. Tingting Liu & Jan Lemeire, 2017. "Efficient and Effective Learning of HMMs Based on Identification of Hidden States," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-26, February.
    4. Maruotti, Antonello & Punzo, Antonio, 2017. "Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 475-496.
    5. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    6. Benaglia, Tatiana & Chauveau, Didier & Hunter, David R. & Young, Derek S., 2009. "mixtools: An R Package for Analyzing Mixture Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i06).
    7. Weiliang Qiu & Harry Joe, 2006. "Generation of Random Clusters with Specified Degree of Separation," Journal of Classification, Springer;The Classification Society, vol. 23(2), pages 315-334, September.
    8. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    9. J. Hambuckers & T. Kneib & R. Langrock & A. Silbersdorff, 2018. "A Markov-switching generalized additive model for compound Poisson processes, with applications to operational loss models," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1679-1698, October.
    10. Francesco Lagona & Marco Picone & Antonello Maruotti, 2015. "A hidden Markov model for the analysis of cylindrical time series," Environmetrics, John Wiley & Sons, Ltd., vol. 26(8), pages 534-544, December.
    11. Francesco Lagona & Antonello Maruotti & Fabio Padovano, 2015. "Multilevel multivariate modelling of legislative count data, with a hidden Markov chain," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 705-723, June.
    12. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    13. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    14. Douglas Steinley & Robert Henson, 2005. "OCLUS: An Analytic Method for Generating Clusters with Known Overlap," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 221-250, September.
    15. Langrock, Roland & MacDonald, Iain L. & Zucchini, Walter, 2012. "Some nonstandard stochastic volatility models and their estimation using structured hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 19(1), pages 147-161.
    16. Dunmur, A. P. & Titterington, D. M., 1998. "The influence of initial conditions on maximum likelihood estimation of the parameters of a binary hidden Markov model," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 67-73, September.
    17. Iain L. MacDonald, 2014. "Numerical Maximisation of Likelihood: A Neglected Alternative to EM?," International Statistical Review, International Statistical Institute, vol. 82(2), pages 296-308, August.
    18. Ingrassia, Salvatore & Rocci, Roberto, 2007. "Constrained monotone EM algorithms for finite mixture of multivariate Gaussians," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5339-5351, July.
    19. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2017. "Multiple risk measures for multivariate dynamic heavy–tailed models," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 1-32.
    20. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    21. Melnykov, Volodymyr & Chen, Wei-Chen & Maitra, Ranjan, 2012. "MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i12).
    22. Qiu, Weiliang & Joe, Harry, 2006. "Separation index and partial membership for clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 585-603, February.
    23. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
    24. Antonello Maruotti & Antonio Punzo & Luca Bagnato, 2019. "Hidden Markov and Semi-Markov Models with Multivariate Leptokurtic-Normal Components for Robust Modeling of Daily Returns Series," Journal of Financial Econometrics, Oxford University Press, vol. 17(1), pages 91-117.
    25. Delignette-Muller, Marie Laure & Dutang, Christophe, 2015. "fitdistrplus: An R Package for Fitting Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i04).
    26. Gianluca Mastrantonio & Antonello Maruotti & Giovanna Jona‐Lasinio, 2015. "Bayesian hidden Markov modelling using circular‐linear general projected normal distribution," Environmetrics, John Wiley & Sons, Ltd., vol. 26(2), pages 145-158, March.
    27. Langrock, R. & Zucchini, W., 2011. "Hidden Markov models with arbitrary state dwell-time distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 715-724, January.
    28. Antonello Maruotti & Jan Bulla & Tanya Mark, 2019. "Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 19-42, April.
    29. Toby A. Patterson & Alison Parton & Roland Langrock & Paul G. Blackwell & Len Thomas & Ruth King, 2017. "Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 399-438, October.
    30. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
    31. Marie Laure Delignette-Muller & Christophe Dutang, 2015. "fitdistrplus : An R Package for Fitting Distributions," Post-Print hal-01616147, HAL.
    32. Jan Bulla & Andreas Berzel, 2008. "Computational issues in parameter estimation for stationary hidden Markov models," Computational Statistics, Springer, vol. 23(1), pages 1-18, January.
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    3. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).

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